# Arithmetic and geometric sequences: where does their name come from?

Where does the name of these two famous types of sequences come from?

The article Geometric progression of Wikipedia says that the geometric sequence is called like this because every term is the geometric mean of its two adjacent terms. Though it is true, it only reduces the question to: why is the geometric mean geometric (in opposition to the arithmetic mean).

Continuing my investigation on Geometric mean, I was told that a square with the same area than a rectangle with sides $a$ and $b$ has their geometric mean $\sqrt{ab}$ for side. That's again totally true, but a square with same perimeter than this rectangle of sides $a$ and $b$ has their arithmetic mean $\frac{a+b}{2}$ for side!

Thus, my question: Who coined these names? And why? Why is the geometric mean more geometric than the arithmetic mean?